SMB
2008

Summary:
Cancer is a complex, multiscale process, in which genetic
mutations occurring at a sub-cellular level manifest themselves
as functional changes at the cellular and tissue scale. The
importance of tumour cell/microenvironment interactions is
currently of great interest. Both the immediate microenvironment
(cell-cell or cell-matrix interactions) and the extended microenvironment
(e.g. vascular bed) are considered to play crucial roles in
tumour progression as well as suppression. Stroma is known
to control tumor growth and invasion to surrounding tissue.
However, it also prohibits therapeutics from accessing the
tumor cells, thus causing drug resistance. Therefore, a thorough
understanding of the microenvironment would provide a foundation
to generate new strategies in therapeutic drug development.
Currently, it is well known that carcinomas are capable of
modifying stroma through angiogenesis-deriving growth factors,
by altering ECM composition, and by stimulating fibroblasts
proliferation. This evolving process typically requires angiogenesis,
the growth of new blood vessels from pre-existing vessels.
Despite the vast amount of experimental data on the tumor-stromal
interaction, the process by which these cells recruit stromal
cells and alter microenvironment during tumor progression
is not yet completely understood. Consequently, mathematical
modeling has become an effective, supplementary tool in the
quest to understand this complex relationship between tumor
cells and host tissue.

Goal:
This minisymposium will focus on the role of the microenvironment
in cancer: from general tumor growth to breast cancer.

Audience:
This session will stimulate biologists who design and perform
the specific experiments as well as modelers who are interested
in building mathematical models which can improve our understanding
of this area. In addition, enough background/introduction
would be presented for those individuals who are new to the
field, and are interested in knowing more about this fascinating
area.

Computational Models of Cancer Invasion Driven by
Cancer Cells Adaptation to the Microenvironment: Experimental
Parameterization and Validation.
Vito Quaranta (Department of Cancer Biology, Vanderbilt
University)
Within the NCI Integrative Cancer Biology Program, our Center
at Vanderbilt is unique because it focuses on integrating
experimentation with mathematical modeling and computer
simulations at the cell scale. Three mathematical models
were developed:
1) The Evolutionary Hybrid Cellular Automata (EHCA) model;
2) The Immersed Boundary Cell (IBCell) model;
3) The Hybrid Discrete-Continuum (HDC) model.
The EHCA model uses a cellular automata based approach that
considers cells as simple grid points. Each cell contains
a complex neural network that links genotype to phenotype.
The grid itself represents the tumor microenvironment (mE)
and the only variable on this grid, apart from the cells,
is the concentration of oxygen, controlled by a (continuous)
partial differential equation. At every cell doubling, the
inner neural network is copied to the daughter cells, but
with a probability of error. The model captures one component
of cancer progression, the generation of phenotypic variation
within a population of growing cancer cells.
The IBCell represents cancer cells as 2D fully deformable
objects including an elastic plasma membrane modelled as
a network of linear springs that defines cell shape and
encloses the viscous incompressible fluid representing the
cytoplasm and providing cell mass. These individual cells
can interact with other cells and with the mE via a set
of discrete membrane receptors located on the cell boundary.
These receptors control several cellular processes, such
as growth, division, death or polarisation. The mE is represented
as physical forces (to include other cells). With experimentally
derived receptor behavior values, cells go on to build realistic
epithelial structures, such as acini, ducts, tubes. The
outcome of these simulations is not predetermined, but is
an emergent property of the collective behavior of cells,
purely determined by their mechanical interactions with
one another and the mE. IBCell is ideal to capture the transition
to invasion when epithelial structures (acini, ducts) built
or perturbed by cancerous cells become unstable.
The HDC model operates at the cell-to-tissue scale, and
represents growth in a one-cell diameter thick 2D slice
of a generic 3D solid tumor. The mE consists of a 2D lattice
of extracellular matrix (f) upon which oxygen (c) diffuses
and is produced/consumed, and matrix degrading proteases
(m) are produced/used. The mE variables f ,c and m are controlled
by a system of continuous reaction-diffusion equations whereas
the tumor cells (Ni,j) are considered as discrete individuals
(cell automata) which occupy single lattice points (i, j),
hence HDC is a Hybrid between a Discrete and a Continuum
model. In HDC the tumor cell population is heterogeneous,
from 100 randomly predefined aggregates of traits, including
rates of proliferation, death, motility, secretion. HDC
examines: tumor morphology outcomes, traits of phenotypes
best adapted to a local mE, dynamics of the adaptation process,
and influence of a range of different mE on morphology and
adaptation outcomes.

To
populate these models and simulations with empyrical homogeneous
datasets, we adopted a platform cell type, the breast epithelial
cell line MCF10A, onto which we established a collection
of variants with distinct invasive potentials, generated
by transfection of oncogenes or multiple passaging in vivo.
We measured many cell parameters, including: oxygen consumption/hypoxia,
proliferation, survival, matrix degrading enzyme secretion,
morphology patterns in 3D culture.
The EHCA model presents an opportunity for parameterization
and validation via an interface with gene expression profiling
high-throughput data from these cell lines, which we are
currently exploring. The IBCell is being tuned with 2D and
3D growth data from MCF10A cells and derivatives, to test
its ability to predict receptor value ranges that lead to
acquisition of invasive morpholgy when ErbB2 growth factor
receptors are overexpressed or overactive.
For the HDC model, initial simulations with these homogenous
datasets are consistent with its prediction that, in order
to occur, invasion requires active competition between phenotypes
with distinct adaptive traits. To empyrically validate these
HDC predictions in vitro, we developed a novel Island Invasion
Assay (IIA), which closely mimics the spatial 2-D arrangement
of growing tumor cells in the HDC model. Preliminary results
suggest that IIA also supports the HDC predictions concerning
invasion (fingering) under stressful tmE conditions. In
addition, some unexpected results point to novel features
that could be included in the HDC model to increase realism.
This is an excellent example of synergistic interactions
between modeling and experimentation, which will hopefully
produce novel insights in the mechanisms underlying cancer
invasion.
For in vivo validation, we are comparing orthotopic mE versus
subcutaneous mE xenografts of the MCF10A tumorigenic variant
lines in mice. Tumor specimens are biopsied at fixed volumes
(0.5, 1 and 1.5 cm diameters) for ex vivo analyses, including
histology to assess invasion, immunohistochemistry and immunofluorescence
to measure cellular proliferation (BrdU incorporation),
apoptosis (TUNEL) and hypoxia (hypoxiprobe). Initial results
reveal unexpected correlations between in vivo mE and tissue
of origin of the cell lines tested (breast gland).
This overall strategy for parameterization of tumor models
and validation of their predictions will be discussed in
the context of our efforts to build, in line with the ICBP
goals, a mathematical oncology group that integrates experimental
biologists with physical scientists on equal foot, and produces
theory-driven experimentation as well as experiment-driven
theory.

Mathematical
and computational modeling holds great promise for personalized
medicine to predict outcomes such as tumor metastasis or
drug response. However, the first step is to show that data
can be incorporated into models and make reasonable predictions.
I will discuss our efforts in experimental parameterization
of a model of tumor progession and the role of microenvironmental
resource limitation in promoting tumor aggressiveness.

We will present some mathematical modelling of the potential
effects of acid production on the ability of tumour cells
to invade tissue and for the selection of certain mutations.
The models will range from very simple partial differential
equation type to hybrid cellular automata.

In order to understand the role of fibroblasts/myofibroblasts
in the early evolution of breast cancer in vitro we developed
a mathematical model as well as conduct experiments. In the
experiments tumor cells are placed on one side of a membrane
and fibroblasts are placed on the other side. The membrane
is semi-permeable, allowing only growth factors such as EGF,TGF-beta,
but not cells, to cross over. The mathematical model describes
the dynamics of the various concentrations of cells and growth
factors by a system of partial differential equations. The
prescence of extracellular matrix have an effect on tumor
grwoth. We demonstrate a good agreement between the simulation
of the model and the experiments.

(this
talk has been cancelled)

M
for Invasion: Morphology, Mutation and the Microenvironment
Alexander Anderson (Department of Mathematics, University
of Dundee)
Cancer is a complex, multiscale process, in which genetic
mutations occurring at a sub-cellular level manifest themselves
as functional changes at the cellular and tissue scale. The
importance of tumour cell/microenvironment interactions is
currently of great interest - both the immediate microenvironment
(cell-cell or cell-matrix interactions) and the extended microenvironment
(e.g. vascular bed) are thought to play crucial roles in both
tumour progression and suppression. In this talk we will present
two different models that examine the selective pressure a
changing microenvironment exerts and how this impacts both
up the evolutionary dynamics of the tumour population and
the morphological changes that occur.